Archive for December, 2012

Call the Doctor

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It was probably only a matter of time (pun intended) before at least one of the kids discovered the world of Doctor Who. It was a slow build for us; some of the other kids in the fifth-grade class H and E part-time in had started watching, some picking up in the David Tennant seasons, others climbing into the newer Matt Smith episodes. I myself hadn’t watched any iteration of Doctor Who since Tom Baker’s Fourth Doctor, and I decided to give it a try with them. By turns witty, poignant, touching and exciting, Doctor Who is everything I remember it being, with all the benefits of 21st-century CGI added into the mix.

The more we watched, though, the more I found E (in particular) identifying closely with the Doctor. That was probably inevitable; he’s quite obviously some flavor of gifted, or perhaps all Gallifreyans are as bright as he, or perhaps he simply benefits from the compended wisdom of close to a thousand years’ existence. Regardless, E instantly fell in love with him. (It’s a little disconcerting when your nine-year-old daughter describes anyone as ‘hot,’ but I suppose I’ll take a Matt Smith/Doctor crush over Bieber Fever.) Still, I couldn’t quite put my finger on what it was about the Doctor’s character that E was finding so appealing and comforting, until we sat down as a family and watched “Vincent and the Doctor.” Then it hit me: where else is she going to find a truly asynchronous protagonist in pop culture?

The Doctor lives in a Gordian knot of asynchrony during the Matt Smith seasons; his wife, the engaging River Song, is actually living her life backwards from the Doctor’s perspective, so each time they meet she knows more about him and he knows less about her. The Doctor himself is killed at the beginning of season six, only to arrive on the scene moments later, a full two hundred years younger, having had the good sense to work out a means by which his companions can investigate his own death once it’s occurred, with a younger version of himself along for assistance. (And let’s not even get started with the paradox of the sonic screwdriver and the Pandorica.) It’s all delightfully madcap, and through it all, the Doctor maintains a gallantry and cool charm that E has found truly enthralling. It’s OK, in the Doctor Who universe – cool, even – to be asynchronous.

I’m glad that voice exists for her. Asynchrony is, from my perspective, the most difficult thing about being a gifted child.  Nine-year-old E – “9E,” for the sake of brevity – comes and goes. Most of the time, she’s solidly ‘teen E,’ more content circumnavigating a playground’s outside path than playing within it. But while she often rolls her eyes at the activities of typical ‘nines,’ she’s usually good for a Saturday morning bowl of Cocoa Puffs and some Phineas & Ferb. We’ve seen a lot more of 12E lately; she’s a little authoritarian with her siblings sometimes, and more prone to exploring some of the more – ahem – mature content residing in our Kindle Cloud account. 14E is handling Algebra I quite nicely, but this new, mathematically-patient E is a very recent iteration, and it’s taken her most of the fall to round into form. We aren’t quite sure what age E is writing at; based on her ACT and EXPLORE scores, that iteration is somewhere between 16E and 19E, and I daresay even 20E has shown up in our critical reading sessions from time to time.

All of these entities have to coexist within 9E’s physical form. I don’t envy her. As a 43-year old guy, I’ve finally reached the age when I’m not seeking to be accepted by anyone for being any age older than my own. (Although many mornings, I’d prefer to be twenty years younger, especially after horsing around with the kids all day.) But E’s just starting down that road, her mind variously projecting iterations of herself five and even ten years older than her biological age, with those iterations often coming and going within the space of an hour. It’s as alienating for her as I remember it being; chronological peers aren’t always where you are intellectually, while your intellectual peers are uncomfortable with you socially. Expectation-setting is a catch-22 for all of us. Do I assume she’ll default to her most mature and intellectually-proficient iteration, and her ‘true age’ moments are aberrations? Do I assume she’s 9E with occasional visitations from the Ghosts of Future E? Do I mentally average all of these iterations and assume she’s 14 years, seven months, or some other such amalgam? In truth, I can’t do any of these things. It’s left to us to merely accept her in whatever iteration the moment and the subject find her, and address her in a manner appropriate to that age. She’s unstuck in time, a gifted Billy Pilgrim, and chasing her across these various iterations during the course of a given day makes me wish for a sonic screwdriver of my own. (Or just a screwdriver.)

I suppose I’m not surprised, then, to find her glued to the wildly asynchronous Doctor’s adventures, hand drifting unconsciously to the popcorn bowl as Matt Smith visits Renaissance Italy and a deep-drilling mining operation in the future and sad Vincent van Gogh himself, his work unappreciated in his time until he’s shown a glimpse of his fame in our own present. Companions come and go in the Doctor’s world, and perhaps that’s by design; asynchrony, whether you’re in a TARDIS or a suburban frame house, is a lonely path. No two humans are alike, but it’s rare that two asynchronous, PG kids can operate in the same relative time long enough to even build a stable friendship. In many ways, I think E wishes it could be as simple as the Doctor’s life is, with the rubber monster of the week or the metallic cybernetic menace of the moment dispatched with thoughtful elegance in every hour’s episode. Perhaps it would be easier for her. But until age gifts her unity, as it has for me, I wish her the very best of every age she’s in.

The Afterglow of Holiday Intensity

Ah, Christmas afternoon. The presents have been opened, brunch has been consumed, and we have enjoyed time with all of our relatives, both near and far. After good-byes and thank-yous, they have all headed out to their next destination. Time to sit down, pour some Christmas cheer (in the form of Baileys and cream), and seriously geek out with our new presents.

Dave and E are playing a game of Doctor Who chess, A is jumping around as an Avenger on the Xbox Kinect, H is playing with her new American Girl doll wearing her T.A.R.D.I.S. shirt, and I am hunting for a new book on my Kindle. Intensities were bundled up for the morning, rolled and wrapped in thick Christmas paper, and taped up tight. It’s not that our extended families don’t have their own intensities – they do – but putting all of our emotional, sensory and psychomotor intensities on display, mixed in with holiday goodies (read: sugar) during a family get-together on Christmas, is more than Dave and I can really handle.

So, we have developed our own Christmas afternoon tradition. Unwrapping our intensities is the last thing we do on Christmas, as the collective house breathes a sigh of relief. We tear open our emotional intensity boxes first, and joyful exuberance bursts into the room. Psychomotor intensity comes next, the box feverishly hopping around the room before finally being freed from its constraints to run whooping loudly through the house.  Soft blankets come out, and backs and feet are rubbed as we open our sensory gifts. And finally (finally!) our imaginational and intellectual intensities take flight as we explore all of the wonderful presents we gave each other, and received.

We can talk excitedly among ourselves about how cool the gifts are, play with each one individually, and examine the nooks and crannies of each piece. We don’t have to explain to anyone what it is, or why we like it so much, or feel so strongly about it. We all just know. The light in our eyes during these moments is more than just excitement; it’s knowing that someone truly understands us, and love and embraces us for who we are.

It’s in these moments that I genuinely see our family’s intensities as the gifts they are, each one worthy of unwrapping, sharing, and celebrating. I’m so glad we opened them today.

After You



Update to this article 1/10/13: We’ve received a ton of emails and messages asking about swapwriting as a service, and we’re very excited to announce that we’re going to start offering remote swapwriting sessions through Google Docs. Click here for more information.


I’m sometimes asked if there are any genuinely different teaching methods that we use in our homeschooling setting. The broad answer is that, since I’m often teaching individually, I can essentially tailor the day’s work specifically to the child involved. E prefers to be a genuine co-investigator, so I’m fairly free to tackle subjects well above my own head with her; there’s no shame in admitting that I don’t know a great deal about, say, mesopelagic feeding  dynamics when I’m fairly sure E already knows that I don’t. H, on the other hand, likes the feel as if there’s a safety bar firmly clicked into place on the ride we’re on, so I usually plan out our work a bit more beforehand, and I try to make sure she always feels like we’re on a safe journey.

Regardless, once we get down to work, a lot of what we do looks a great deal like the work in any school setting: there are keyboards clacking away, printers whirring into action, questions being asked and answered (sometimes) or collaboratively tackled (more often). Most of what we do wouldn’t be out of place in any traditional school classroom. There is one thing we do very differently, though. It works remarkably well, and I’d be remiss if I didn’t mention it at some point in our blog work. That one thing is swap-writing.

Swap-writing, at its most basic, works like this: I start a document in Google Docs, and share it with whomever I’m swap-writing with; sometimes H, sometimes E, sometimes both. We decide on a rough genre – we might choose to write fantasy, for instance, or horror, or modern midweight school-age fiction. One of us gets things rolling, and then it’s a collaborative effort, each of us taking turns writing some amount between a sentence (the minimum) and a short paragraph (the maximum). Rules are fairly minimal. We’re obligated to support each other; other writers’ ideas are valid unless there’s a better idea offered; and we take tone from each other. In other words, there’s no fighting to make a tragedy a comedy, or vice versa, and we work with what we’re given by our co-writer. If E places us in Transylvania, that’s where we’ll be (for a while, anyway); if H wants to write in first person, that’s the style we’re writing in.

Swap-writing, I’ve found, has at least four advantages over the write-a-page-and-turn-it-in model.

  • First, feedback occurs in real-time, during the act of writing itself. I’m a big believer that improvement in anything happens through direct, real-time interaction. We become used to that as adults; we don’t submit videos of our flyfishing casts for later review, or phone-camera snapshots of our golf swings. The ubiquitous paint-with-a-glass-of-wine event venues that have sprung up in the past few years count on the concept of real-time interaction as their modus operandi, and so do poetry slams and open-mic nights and any number of other artistic and athletic endeavors. We want to be told, right now, what it is that we’re doing right and wrong. How, then, did writing become this evaluated-at-a-distance concept? Simple. It’s far easier for a teacher with a classroom of 28 kids to solicit work and grade it later. It’s a reality of the system we’ve built – but that doesn’t mean it’s the right way to teach writing. Every kid I’ve worked with in our family in a swap-write setting has almost immediately shown me some areas of their work that need help – and it’s far easier to stop in midsentence and correct something, as we’re writing together, than to try and instill good writing habits in someone who’s already finished the work. Grading your cake poorly, in other words, doesn’t help you become a better ingredient measurer and mixer. That happens while the cake’s being made.
  • Second, it’s easy to focus effort on areas of writing that need work. H and E have usually had very different writing challenges at any given point in their development as writers. They’re both fantastic writers, but where H will sometimes rush to get to the next plot point – “and then they arrived at the mountain” – E will occasionally get bogged down in the detail. Working individually with each of them lets me target those habits and work them extensively – and it gets even better when the three of us write together, because I can act as a fulcrum between their two respective writing paces. (They also start regulating each other, which is a marvelous thing to watch.) But if I see one of them rushing the pacing, or dawdling the story, or flinging out too many plot hooks, I can focus in on that area through my own participation in the swap write, insisting on detail, curtailing blind plot avenues, and asking them to police their own writing through what I write, too.
  • Third, it pulls everyone’s work up to a common level. Having assigned a few dozen writing prompts in the early months of our homeschooling/unschooling work, intermixed with swap-writes, I noticed something interesting. Both H and E’s writing in writing prompts was – initially – nowhere near the quality of their writing in a swap-writing environment. Writing-prompt quality went up steadily the more we swap-wrote together, and continuing to use writing prompts provided me a reasonable measure of their ‘blank sheet of paper’ abilities. But the improvement came through swap-writing, and after a while, I realized why: they were trying to uphold the quality standard being set. E was trying to ‘write up’ to where I was, and H was trying to ‘write up’ to us both. Adding something to an existing work at a particular quality level, in other words, was pulling them up to that level, sinceno one wanted to let down the overall writing quality of the piece.
  • Finally, it’s creative and fun. The swap-writing environment is pure improvisational jazz – it encourages on-the-spot creativity, rapid reaction to the work of others, and a collaborative mindset in which everyone gets a chance to ‘solo’ and everyone spends time in the rhythm section. They also know that the fundamental rule is that we can go wherever they’d like to go, as long as they write creatively, correctly, and supportively. We’ve had a swap-writing session that began in a pizza parlor and swiftly evolved into zombie-comedy; H and E kept pulling the topic in that direction, and so long as their writing quality remained high, I was more than willing to go with them. Some swap-writes have been one-shot exercises, little forty-minute vignettes that came to a natural end; others have evolved into full-on novellas that have now been running for months. Both are fine by me.

What’s really interesting for the girls is that there are many examples of professional swap-writing out in the literary world proper. Several of my favorite authors, including Neal Stephenson and Greg Bear, are effectively swap-writing the Mongoliad series, and for a time the work was being released a chapter at a time, serial-fashion. That’s an inspiration for both H and E, and I can also point them back toward several top-notch swap-written novels of the past – most notable Pratchett and Gaiman’s excellent Good Omens, and Niven and Pournelle’s The Mote in God’s Eye. These books make for great critical-reading sessions, too. We’ll read some precursor works by each author, and then discuss how each one influenced the final, created whole, and where each authors’ stylistic ‘fingerprints’ are most evident.

Swap-writing isn’t for everyone as a homeschooling instructional technique. It’s time-intensive, and intellectually demanding, and it will most certainly push your own writing abilities as it pushes your kids’. But the rewards, in terms of writing improvement for children, are immense and long-lasting. The major strides I’ve seen in both H and E’s writing this year have come from swap-writing, coupled with independent work (traditional writing prompts). Not sure if it’s for you? Give it a try. There’s no cost to set up a Google Docs account, and no problem if you’re swap-writing on a single computer, either; everyone can just take turns at the keyboard.  If nothing else, I guarantee you’ll have some fun with your kids, and you might just find it to be a creative and enjoyable hobby for your entire family.

Cthulhu on the Island of Misfit Toys

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It’s possible, at the moving-walkway pace of modern life, to grow a bit insular with your own family – to come to accept your own familial day-to-day existence as the norm. It’s probably like living next a train station in the city. In Chicago, they’ll tell that ‘the more you hear the train, the less you hear it.’ That’s kind of how it works. Intensities become normal over time; quirks and idiosyncrasies become familiar, because…well, because they are familiar. You don’t feel like the Island of Misfit Toys when all you see all day are jelly-shooting squirtguns. I’d probably be alarmed to see round wheels on a train at this point, or a correctly named jack-in-the-box.

Then there’s moments like last night, when we attended Kathy’s department dinner for her medical group. Lots of bright, witty adults. Lots of bright kids running around; I spotted a MATH OLYMPICS t-shirt on one. Lots of drinks consumed, and lots of hors d’oeuvres. Docs talked shop, and spouses did our best with the usual small talk, although most are aware of our situation and that tended to turn most interactions toward homeschooling.

And then…the white elephant exchange.

Y0u’ve been to a hundred of them, and they normally pass without much in the way of notable incident. There are oohs and aahs for the good gifts; fists are brandished in mock-seriousness as others threaten to steal those later. Recipients of the truly unfortunate receive sympathetic comments and peanut-gallery guffawing in equal measure. This white elephant exchange was largely no different. The fleece blanket we brought was stolen right up to the maximum of three times, as was an indoor s’mores maker. A wicker chip-and-dip was advertised as eminently stealable with mounting vigor. The man next to me, recipient of a plastic daisy with a built-in calculator, shook his head and sadly contemplated his lot. I was whiling away the time, encouraging the woman next to me to go steal the s’mores maker again, when my wrist was seized in a tiny, iron grip.

“Dad.” It’s E’s insistent whisper. “Look.”

There he was, in all his plush glory; Cthulhu himself, in plush backpack form. There was a single moment of absolute quiet while the room labored, as a group, to come to grips with this thing. What resulted, however, was  immediate confusion. One person thought it was an octopus, and not a very cute one at that, while another insisted it was the Loch Ness Monster, and indeed, the latter became its label for the evening. The woman who opened the big C did her best to sell a socially-acceptable facial expression, but clearly wanted nothing to do with him.

But E did. In a big way.

By way of backstory, E began reading Lovecraft last fall for the work we were doing together in Victorian and early 20th-century horror, and became a lover of all things Cthulhu in pop culture. When The Doom That Came to Atlantic City was announced on Kickstarter, she was fairly rapturous about acquiring it. And now here he was, in backpack form, no more than ten feet from her, and no one in the room even knew it was him. (It?) This would have been a destination gift for her – a Christmas-list item – and she seemed confused as to how it could possibly have ended up here, unwanted, among the scented candles and picture frames.

E was shocked. “Dad,” she whispered again. “It’s Cth-”

“Don’t say it aloud,” I whispered back, partly as a joke – in Lovecraft, you’re not supposed to say the Great Old Ones’ names aloud – but also because, on the off chance there was another Lovecraft fan lurking in the room, I suppose Cthulhu could’ve been stolen away. Based on the vigor with which my wrist was being gripped, and the wide-eyed expression E had on, I kind of didn’t want that to happen.

So the woman did her best to pimp out the backpack as numbers were called, going so far as to begin waving his claws about and giving his tentacles a festive dancing rhythm, but no luck. And thus did #18 come around, our number, and H valiantly stole him away from a greatly-relieved gift recipient. They huddled over him, doing their best to disguise the fact that they’d won him, and took turns asking me ‘how many numbers are left?’ But water bottles and crappy earbuds were grudgingly accepted, and the s’mores maker was stolen one final time, and that was that. We emerged into the cold Denver night with our Great Old One in backpack form, their breath coalescing into vaporous clouds as they danced joyfully down the street to our car, holding Cthulhu aloft. Neither one could believe they’d made off with this prize; it was as if they’d taken home a Renoir original no one had recognized for what it was.

“Even among misfits,” Yukon Cornelius once sagely noted during his time as a Rankin-Bass Production, “you’re misfits.” There we were, among brilliant but sometimes socially-awkward doctors and their brilliant but sometimes socially-awkward kids, and the whole room came to a stop because E and H were getting the vapors by turns over a stuffed monster backpack. Suddenly, our square wheels and jelly-shooting were on display once more…but it didn’t really bother me. We’re happy on the Island; it’s noisy, but it’s our noisy, and it’s odd, but it’s our odd. And what was more important to me was that it didn’t bother them at all.  That’s part of the goal, I think, as parents of gifted kids; we’re trying to make sure they end up comfortable in their own skin.

Based on the gleeful, unencumbered grin that H wore as she set off for school this morning – an Elder God grimly conveying her expandable file and calculator and pencils for her – we’re off to a good start.

Waves of Intensity

They didn’t remember the ocean.

I was sure they would, but they didn’t. It’s one of those strange artifacts that comes along with raising gifted kids; they have incredible memories for some things; A can tell you everything about the Clone Wars, but doesn’t remember his ornament from last Christmas. Even the girls have just recently begun to recall things from years past. Much of the time, when their various intensities aren’t recording memories for them, they’re just kids of their own specific age – kids for whom the general RECORD button of life has only recently lit up. So, despite having been to Hawaii multiple times as toddlers, and to San Diego in 2010, it was all new again for them when we returned to San Diego this week. New…and wonderful.

I’ve never thought about the ocean from the perspective of intensity, but it’s all there – sight and sound and touch and smell and taste. The sensation of wet sand between your toes, the sucking of the tide, the roar of the waves crashing, the humid salt air, the tang of brine when a wave crashes funny and serves you an unexpected mouthful. Imaginational comes to the forefront for H; ‘let’s pretend we’re on the only tiny island in a world of water!’ Psychomotor bursts forth onto the beach for A, and I have to go into an impromptu sprint and get him by the arm at the water’s edge to remind him that he can’t go in too deep. Part of me wanted to go in with him, though;  I’m 43, and I still find the ocean a wondrous and amazing thing. For them, it was nearly overwhelming this time.

Intensity comes along on vacation. It might as well have had its own checked bag. From Legoland (where A quite unexpectedly self-identified as a coaster junkie) to the Birch Aquarium (where H and E wept silent tears over the newborn moon jellies), it was everywhere.  We all had a good laugh when we encountered a knob labeled INTENSITY in a jet cockpit on the USS Midway; we all know what we are, and we can laugh about it. But the ocean captivated them all like nothing else.

It was great fun to watch them interact with it, to bring all of their norms of engagement into play with this immense, ever-moving force. They don’t know that beach sand is stealing a little extra kinetic energy with every step, or that the tide patiently waits to pull them seaward as they run among the tidepools, or that the day slips away in the soft California sun faster than we’re used to; so the entirety of their afternoons was exertion. They ate like rescued castaways every morning and slept like infants every night, exhaustion overtaking them in the way it did when they were tiny, leaving them sprawled, still in their clothes, as the sand dried quietly and fell to the carpet below. We had to walk them to the bathroom, get them into their pajamas, and see them back to bed like we did when they were two.

The ocean was more intensity than they themselves had in them, and seeing them confront this vast, implacable force of stimulus – and cheerfully losing the energy battle each day – reminded me of why parenting gifted children is such a joyful, but exhausting, exercise. They are the ocean within our home, never resting, always in motion, threatening to leave us with no energy to spare while the tide keeps rolling in and out with measured regularity, question after question, tears and shouting and laughter all taking their turns. And while I’d very much like to conserve my energy – taking short steps in their fine sand instead of long, loping strides, staying ankle-deep in the surf – to do so is to deny the nature of the thing.  The beach was meant to be run along joyfully, and the tide met with measured resistance, energy for energy – like for like.

I suppose I wouldn’t have it any other way.

I Think I’ll Just Calculate the Product, Thanks


I’ve said it before, regarding perfectionism, and I’ll say it again, this time regarding estimation: that word…I do not think it means what you think it means. After our last estimation post became a polemic, with opinions piling up in our inboxes on both sides of the argument, I wanted to take a moment and add my perspective on it. Specifically, I want to make sure we’re talking about the same educational construct.

First, estimation isn’t rounding – at least, it’s not rounding the output of a problem. Rounding is the mathematical truncation of a decimal number from more place values to fewer. Rounding outputs – results of mathematical problems – is a fairly valuable skill, especially when significant digits come into play. If I’m working with raw data that comes in from one source to the nearest tenth, and from another source to the nearest thousandth…well, I’m going to have to report up to the client in tenths; that’s the greatest level of precision I received in the combined sets of values. Or I might want to know about how many unit sales of a product were made last month; I can take that output to the nearest hundred thousand, please. No one’s debating the relative merits of learning to round output numbers.

Second, estimation also isn’t prediction. Prediction is a guess of an unknown future number. It’s where I call my wife from the grocery store and ask about how many people might be coming to the dinner party; if it’s more than twenty, maybe I’ll need two bags of ice. If less than twenty, probably one. I don’t know the total, and I likely won’t have the final data in hand until the last time the doorbell rings. I’m asking for an educated guess as to what might happen. We all use predictive skills, every day, and no one’s talking about taking a baseball bat to the honored tradition of a rough guess.

Third, estimation isn’t sampling and extrapolation, either. If I’m killing time with a friend in Lower Downtown Denver and we decide to try and figure out how many people walk past our cafe storefront in a day, we could sample the number that walk by in a ten-minute period and multiply out through the business’ operating hours. That’s not estimation by the definition of modern elementary-school math. Sampling and extrapolation have obvious uses in day-to-day life, most notably for those of us engaged in using past data to model possible future events.

Finally, estimation isn’t a reasonable guess as to a number – the ubiquitous jar-full-of-gumballs problems tossed out frequently. Guessing what a number might be, without any attendant input information (“this jar is twenty centimeters tall and has a circumference of 14 centimeters”) is just that – a guess. We know there aren’t two hundred billion gumballs in the jar, and we know there aren’t twelve. It’s somewhere in between, and we can probably use our own experience in life to get within a hundred or so of the answer. Guessing how many gumballs are in a jar doesn’t have a great deal of use in life, either, but it does form the basis of a whole category of retail and Facebook contests.

Estimation1, for those not currently teaching an elementary school-aged child, is a different animal. It’s where we provide a very typical, straightforward math problem to someone trained either to solve the problem by hand, or use a calculator to come up with the right answer. We then ask them to do neither, but rather just kinda take a rough shot at it, neither a true guess (which would have no inputs, and require no work, but also have no value) nor an answer precise to any specific level (which would require actual work, but yield a precision result). Instead, we’re asking a child to combine the worst aspects of both: do some work to yield a result with little value.

Estimation problems go like this: estimate the product of 347 and 13.

What my kid is supposed to do is decide that 347 is pretty close to 350, and 13 is pretty close to 10, and come up with an estimate of 3,500. Doesn’t that sound neat and orderly? It’s got to be around 3,500, because both of my estimate numbers were pretty close to the original numbers – right? But that’s not actually true. The answer isn’t anywhere near 3,500 – in fact, it’s off by more than a thousand. The right answer is 4,511.

Now, in what universe is the 3,500 estimate valuable? Take science, law, engineering, medicine, and business right off the board. If the bridge cables have to weigh less than 4,000 pounds in total to keep the bridge aloft, and I turn in my ‘estimate’ of 3,500, I’ve probably sent an entire rush hour’s worth of commuters into Lake Washington. If the patient must receive no more than 4,000ml per month of medication, I’ve probably put him in a pine box. There are professions that need the right answer, and only the right answer, and the ‘estimate’ was nothing more than a waste of a few seconds that could have been used finding a calculator. Worse yet, we encouraged you to do this by telling you that you’re good at estimation in elementary school. You’re not. None of us are. And the last thing we want is to encourage professionals to keep after this lunatic waste of time as they enter their chosen fields of work.

So maybe it’s useful in real life. Except it’s not. ‘I use estimation all the time at the grocery store,’ I read in the comments on the original estimation post. Really? Are you keeping a running log in your head of how much your grocery purchases cost? That seems like a great deal more work than totting them up on a calculator as you go. If, that is, you care about the pre-checkout cost – since the store is going to provide you an itemized receipt after the fact. Maybe what you meant was approximation – “there’s sixteen people on the soccer team, but not all of them show up every week; still, CapriSuns come ten to a box, better get two boxes.”

So why are we doing this? There’s no question estimation is quick, but it’s also wrong, and it provides us with a false sense of confidence in our own estimation abilities. Sometimes that’s mostly harmless, as Douglas Adams would say; and sometimes, as Kathy pointed out in her post, it’s potentially deadly. I suppose my question is this: what sort of mathematical questions do we encounter in day-to-day life that we’re both unwilling to calculate through and comfortable with our answer being wildly wrong? If we’re looking for an alternate form of math to teach our kids, one that emphasizes mental calculation, why not replace estimation with something useful – like Vedic math? At least they’d end up with the right answer in exchange for their time and effort.


1 Ironically, we’re not even using these terms correctly; what modern math calls estimation is really approximationEstimation is, technically, making an educated guess – ‘how many gumballs do you think are in this jar?’  – while approximation is making a measurement or count specific enough for a given purpose. Guessing that the flagpole on top of a building is ten feet tall is an estimation. Measuring that flagpole as being ‘about’ ten feet tall is an approximation.  This isn’t helped by the fact that Merriam-Webster defines ‘estimate’ as ‘to judge approximately.’ But I won’t even get into that here.